This project is intended to increase our understanding of the use and application of mathematical and statistical models in toxicology and biochemistry and to implement new mathematical models to aid in explaining current research findings. The research effort explores a diverse range of biological areas, including carcinogenesis, pharmacology, developmental biology, neurology and immunology. In cancer modeling, major accomplishments include (1) two new models of carcinogenesis were studied in detail (a model with true stem cells for skin carcinogenesis and a multipathway, multistage model for studying colon and liver cancer); (2) development of new methods for utilizing data on malignant and premalignant states when building a mechanistic model; (3) applying mechanistic models to data on premalignant lesions and tumors simultaneously; (4) the development of a general algorithm for estimating tumor incidence from arbitrarily complicated multistage models and (5) developed methods to link PBPK models to tumor incidence models. In physiologically-based pharmacokinetic modeling, this group has (1) substantially improved a PBPK model for TCDD and applied it to study TCDDs effects on thyroid hormone metabolism; and (2)developed rules for using mechanistic models in risk assessment. In risk assessment, this group has (1) collaborated with EPA on the reasessment of TCDD; (2) developed code for estimating benchmarks doses using a profile likelihood.